In the lag compensation design procedure, why is the desired phase margin increased by an additional 5 to 12 degrees?
Explanation
Although a lag compensator is designed to have minimal phase impact at the new gain crossover frequency, it still introduces a small amount of negative phase (lag). To counteract this, the target phase margin is increased slightly to ensure the final compensated system achieves the desired margin.
Other questions
What is a primary advantage of using frequency response design techniques for lead compensation over root locus methods regarding steady-state error?
In the context of transient response design via gain adjustment, what is the relationship between phase margin and percent overshoot?
In Example 11.1, a 9.5 percent overshoot is required. What is the corresponding required phase margin for a damping ratio of 0.6?
In Example 11.1, after determining a required phase margin of 59.2 degrees, at what frequency on the phase plot does this phase margin occur?
According to Example 11.1, what is the magnitude of the system on the Bode plot at the phase-margin frequency of 14.8 rad/s, and how much gain adjustment is needed?
What is the final calculated preamplifier gain, K, for the position control system in Example 11.1 to achieve a 9.5 percent overshoot?
What is the primary function of a lag compensator as visualized on Bode diagrams?
In the lag compensation design of Example 11.2, a tenfold improvement in steady-state error is required over a system with Kv = 16.22. What is the new required Kv and the corresponding gain K?
In the lag compensator design of Example 11.2, how much attenuation must the compensator provide at the new phase-margin frequency of 9.8 rad/s?
What are the primary effects of a lead compensator on a system's frequency response, as described in the section on visualizing lead compensation?
In the lead compensation design of Example 11.3, a peak time of 0.1 second and a 20 percent overshoot are required. What is the calculated required closed-loop bandwidth?
For the lead compensation design in Example 11.3, what is the required total phase contribution from the compensator, including a correction factor, to achieve a final phase margin of 48.1 degrees?
Based on Example 11.3, what is the value of beta (β) for a lead compensator that must provide a maximum phase shift of 24.1 degrees?
In the lead compensator design of Example 11.3, what are the calculated break frequencies, 1/T and 1/(βT)?
When designing a single passive lag-lead network, what is the relationship between the parameter α (from the lag network) and β (from the lead network)?
In the lag-lead compensation design of Example 11.4, a system with G(s) = K/(s(s+1)(s+4)) requires a Kv = 12. What value of gain K is needed?
In the lag-lead compensation design of Example 11.4, what is the estimated value for gamma (γ) to obtain the required 56 degrees of phase shift from the lead compensator?
For the lag portion of the compensator in Example 11.4, what are the designed higher and lower break frequencies?
What is the primary purpose of using a Nichols chart in control system design?
In the lag-lead design using a Nichols chart in Example 11.5, what is the required peak amplitude, Mp, in dB for a 20 percent overshoot?
In the Antenna Control Gain Design case study, what is the calculated phase margin required to achieve a 20 percent overshoot?
For the Antenna Control Gain Design case study, what is the required gain K to achieve the 20 percent overshoot, given the gain is -34.1 dB at the phase-margin frequency when K=1?
In the Antenna Control Cascade Compensation Design case study, what is the required open-loop velocity error constant, Kv, for a fivefold improvement over the gain-compensated system's Kv of 1.97?
For the lag compensator designed in the Antenna Control Cascade Compensation case study, what are the chosen upper and lower break frequencies?
What is the reason a lag compensator is described as being similar to a low-pass filter?
How does a lead compensator, from a frequency response perspective, increase the speed of a system's transient response?
What is the second step in the design procedure for transient response via gain adjustment?
According to the characteristics of the lag-compensated system of Example 11.2 shown in Table 11.2, what is the actual percent overshoot of the final design?
What is the general relationship between the upper and lower break frequencies of a lead compensator defined by Gc(s) = (1/β) * (s + 1/T) / (s + 1/(βT)) where β < 1?
In the lead compensation design procedure, what is determined in step 7?
According to Table 11.3, what is the actual lead-compensated value for the closed-loop bandwidth in Example 11.3?
What is the reason for selecting a lag compensator's upper break frequency to be one decade below the new phase-margin frequency during design?
In the final lag-lead design of Example 11.4, what is the actual peak time achieved by the compensated system according to Table 11.4?
In the lag-lead compensator design of Example 11.4, the final compensated system has a forward transfer function with a velocity error constant Kv of 12. What does this indicate about the system's steady-state error?
What is the first step in the outlined procedure for designing a lag-lead compensator using a Nichols chart in Example 11.5?
In the Nichols chart design of Example 11.5, after raising the gain to be tangent to the 1.81 dB curve, what is the resulting velocity error constant, Kv, for the plant G(s) = 150 / (s(s+5)(s+10))?
In Example 11.5, the initial gain-adjusted system has Kv = 3, but the final requirement is Kv of no less than 6. How is this improvement achieved in the final steps?
What combination of compensators is required to improve both steady-state error and transient response in a system?
In the Antenna Control Cascade Compensation case study, the lead compensator must contribute a phase of 25.1 degrees. What is the corresponding value of beta (β) or gamma (γ)?
How is the final system gain K typically handled in a lag compensator design procedure?
What is the consequence of a lead compensator on the initial slope of a Bode magnitude plot?
When combining lag and lead compensation, which component is typically designed first and why?
In Example 11.2, the lag compensator's transfer function is Gc(s) = 0.063(s + 0.98)/(s + 0.062). Why is the gain of 0.063 included?
What is the relationship between the closed-loop bandwidth and the speed of response (e.g., settling time, peak time)?
What is the primary trade-off when using simple gain adjustment for control system design?
For the lead compensator defined by Gc(s) = (1/β) * (s + 1/T) / (s + 1/(βT)), at what frequency does the maximum phase lead occur?
In Example 11.3, what is the final gain of the lead compensator Gc(s), given its form is 1/β * (s+25.3)/(s+60.2)?
What is the typical visual effect of a properly designed lag-lead compensator on a Nichols chart plot?
In the final step of the lag-lead design in Example 11.5, how is the required improvement in the static error constant of at least 2 achieved?